I understand your question. I just don’t have the inclination to hold a college level math course. you do need that to understand the math. maybe you don’t realize the complexity of what you’re asking.
basically, numerical/iterative methods for solving polynomials (and anything else you can use a taylor approximation on) work with “fixed points”, and there are criteria (Banach fixed-point theorem) to the fixed point equation that guarantee convergence (if the criteria are met).
the screenshot you posted only calculates values related to the EPS termcrit condition, nothing actually part of the fixed point iteration. that happens earlier.
if you look carefully, these expressions look like derivatives of something that is probably the distortion polynomial: